Sketchup does do this very nicely. If you’d like to keep your same workflow in Rhino you can do the following (counter intuitive maybe but it works):
Cut the blocks you’d like to make unique into a different file.
Make a modification to the block (maybe add a point inside them if you really don’t want any changes immediately)
Cut and paste them back into the original file
Note now they’ll all be called ‘chair 01’ in the blockmanager.